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slamgirl [31]
3 years ago
10

75,000 live bacteria are present in a culture in a flask. When an antibiotic is added to the culture, the number of live bacteri

a is reduced by half every four hours. Approximately how many hours have passed when there are 3000 bacteria left alive
Mathematics
1 answer:
Veronika [31]3 years ago
8 0
N = 75,000*(1/2)^(h/4) . . . . N = number alive; h = hours

3000 = 75000*(1/2)^(h/4) . . . . . substitute given numbers
1/25 = (1/2)^(h/4) . . . . . . . . . . . . . .divide by 75000
log(1/25) = (h/4)*log(1/2) . . . . . . . take the log, then divide by the coefficient of x
h = 4*log(1/25)/log(1/2) ≈ 18.6 . . . . hours

___
Of course log(1/25) = -log(25) = -2log(5), so the expression for h can be written as h = 8log(5)/log(2)
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Write a cubic function whose graph passes through the points (-4,0)(4,0)(0,6) and (2,0)
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Step-by-step explanation:

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2 years ago
Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, nor
kenny6666 [7]

Answer:

a) 0.0167

b) 0

c) 5.948

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 6.16 ounces

Standard Deviation, σ = 0.08 ounces

We are given that the distribution of fill volumes of bags is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) Standard deviation of 23 bags

\displaystyle\frac{S.D}{\sqrt{23}} = \frac{0.08}{\sqrt{23}} = 0.0167

b) P( fill volume of 23 bags is below 5.95 ounces)

P(x < 5.95)

P( x < 5.96) = P( z < \displaystyle\frac{5.95 - 6.16}{0.0167}) = P(z < -12.57)

= 1 - P(z < 12.57)

Calculation the value from standard normal z table, we have,  

P(x < 5.95) = 1 - 1 = 0

c) P( fill volume of 23 bags is below 6 ounces)  = 0.001

P(x < 6)  = 0.001

P( x < 6) = P( z < \displaystyle\frac{6 - \mu}{0.0167})

Calculation the value from standard normal z table, we have,  

P( z \leq -3.09) = 0.001

\displaystyle\frac{6 - \mu}{0.0167} = -3.09\\\\\mu = 6 + (0.0167\times -3.09) = 5.948

If the mean will be 5.948 then the probability that the average of 23 bags is below 6.1 ounces is 0.001.

7 0
3 years ago
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